Diffraction - Revision history

Erik Krause: zenitar and nikkor fisheye comparison regarding diffraction

2011-01-03T22:39:14Z

zenitar and nikkor fisheye comparison regarding diffraction

Erik Krause: /* Resolution */ wide angle

2011-01-03T22:21:21Z

‎Resolution: wide angle

Erik Krause: additional info

2010-12-29T12:43:08Z

additional info

Thomas Rauscher: Fixed math bug. Original formular by Erik

2010-12-27T14:44:34Z

Fixed math bug. Original formular by Erik

Erik Krause: /* Resolution */ clarified

2010-12-25T22:09:13Z

‎Resolution: clarified

Erik Krause: /* Resolution */

2010-12-25T21:33:28Z

‎Resolution

Erik Krause: /* Sharpness */

2010-12-25T20:46:39Z

‎Sharpness

Erik Krause: /* Resolution */ tried to fix math...

2010-12-25T20:34:45Z

‎Resolution: tried to fix math...

Erik Krause: basic page on diffraction regarding panoramas

2010-12-25T20:23:55Z

basic page on diffraction regarding panoramas

New page

{{Glossary|The physical property of light which causes image blur depending from the aperture used.}}

==What it is==
Diffraction in general is the bending of waves around an obstacle. In photography the light waves are bent around the edges of the aperture, causing f.e. the well known star like pattern around the sun if shot stopped down. Since diffraction affects any point of the image (not only very bright sources) it reduces general sharpness and limits effective resolution. Diffraction blurs any point to a pattern called "[[w:Airy disk]]".

==Sharpness==
Diffraction is one of three factors limiting the image sharpness. Second is aberration (f.e. [[chromatic aberration]]) which is determined by lens build quality. Third is de-focus or [[Depth of Field]].

Diffraction depends only on the physical aperture size. Hence it's effect is generally larger the smaller the used sensor is due to the larger magnification of the image. That's the reason why compact cameras can't (or shouldn't) be stopped down further than f/5.6. As a rule of thumb the limit for APS-C sized sensors is f/8 to f/11 and for full frame ones f/16 to f/22.

==Resolution==
The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is:
<math> pixel resolution = /frac {FoV}{asin \left(\frac{1}{1490*D}\right)}</math>
''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in pixels/degree which is obtainable by a given focal length (vertical) and f-number (horizontal):
'''2.8 4 5.6 8 11 16 22 32 44'''
'''50''' 464 325 232 163 118 81 59 41 30
'''100''' 929 650 464 325 236 163 118 81 59
'''200''' 1,858 1,300 929 650 473 325 236 163 118
'''400''' 3,715 2,601 1,858 1,300 946 650 473 325 236
'''800''' 7,430 5,201 3,715 2,601 1,891 1,300 946 650 473
'''1200''' 11,145 7,802 5,573 3,901 2,837 1,950 1,418 975 709
Some usage examples
*You want to shoot a gigapixel panorama of 175° width with a 800mm lens at f/11. You get 175*1,891 = 330,925 pixel maximum horizontal resolution.
*You will use an APS-C format sensor in portrait orientation for this panorama. A 800mm lens has a FoV of 1.1° in that case, which at f/11 gives 2080 pixels or app. 6 megapixels. Applying the 70% rule to compensate for bayer interpolation blur indicates that 12 megapixels per image are enough.

==External links==
*wikipedia on [[w:Diffraction|Diffraction]]
*wikipedia on [[w:Angular resolution|Angular resolution]]
*[http://www.kenrockwell.com/tech/focus.htm Ken Rockwell's page] on Selecting the Sharpest Aperture

@@ Line 32: / Line 32: @@
 ===Wide angle===
 Although the above formula is applicable to wide angle and [[fisheye]] lenses as well it is harder to give correct values. Most DSLR wide angle and fisheye lenses change the entrance pupil diameter depending from the angle of incidence. This is intended and serves as a mechanism to compensate for natural [[vignetting]].
 ==Caveats==
@@ Line 42: / Line 44: @@
 *wikipedia on [[w:Angular resolution|Angular resolution]]
 *[http://www.kenrockwell.com/tech/focus.htm Ken Rockwell's page] on Selecting the Sharpest Aperture
 *A very extensive article about resolution limits on [http://www.luminous-landscape.com/tutorials/resolution.shtml Luminous Landscape] containing many valuable links.

@@ Line 17: / Line 17: @@
   <math> pixel resolution = \frac{FoV}{asin\left(\frac{1}{1490*D}\right)}</math>
-''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors for an ideal lens without aberrations:
+''D'' is the physical diameter of the lens' [[entrance pupil]], which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors for an ideal lens without aberrations:
             '''2.8      4     5.6       8      11      16      22    32    44'''
     '''50'''      464    325     232     163     118      81      59    41    30
@@ Line 29: / Line 29: @@
 *You want to shoot a gigapixel panorama of 175° width with a 800mm lens at f/11. You get 175*1,891 = 330,925 pixel maximum horizontal resolution.
 *You will use an APS-C format sensor in portrait orientation for this panorama. A 800mm lens has a FoV of 1.1° in that case, which at f/11 gives 2080 pixels or app. 6 megapixels. Applying the 70% rule to compensate for bayer interpolation blur indicates that 12 megapixels per image are enough.
 ==Caveats==

@@ Line 13: / Line 13: @@
 ==Resolution==
 The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is:
- [[File:pixelresolution.png]]
+<math> pixel resolution = \frac{FoV}{asin\left(\frac{1}{1490*D}\right)}</math>
 ''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors:
             '''2.8      4     5.6       8      11      16      22    32    44'''

@@ Line 5: / Line 5: @@
 ==Sharpness==
-Diffraction is one of three factors limiting the image sharpness. Second is aberration (f.e. [[chromatic aberration]]) which is determined by lens build quality. Third is de-focus or [[Depth of Field]].
+Diffraction is one of four lens based factors limiting the image sharpness. Second is aberration (f.e. [[chromatic aberration]]) which is determined by lens build quality. Third is de-focus or [[Depth of Field]]. Fourth is motion blur due to lens shake.
 Diffraction depends only on the physical aperture size. Hence it's effect is generally larger the smaller the used sensor is due to the larger magnification of the image. That's the reason why compact cameras can't (or shouldn't) be stopped down further than f/5.6. As a rule of thumb the limit for APS-C sized sensors is f/8 to f/11 and for full frame ones f/16 to f/22.
@@ Line 12: / Line 12: @@
 ==Resolution==
-The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is:
+The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. We can safely assume the equivalent of one pixel distance as the minimum resolvable distance required by the Rayleigh criterion. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution.
-<math> pixel resolution = \frac{FoV}{asin\left(\frac{1}{1490*D}\right)}</math>
-''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in '''pixels/degree''' which is obtainable by a given focal length (vertical) and f-number (horizontal) without regard to currently available sensors:
+For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm which is in the middle of the spectrum and a color where our eyes are most sensitive. The resulting formula is:
             '''2.8      4     5.6       8      11      16      22    32    44'''
     '''50'''      464    325     232     163     118      81      59    41    30
@@ Line 23: / Line 25: @@
    '''800'''    7,430  5,201   3,715   2,601   1,891   1,300     946   650   473
   '''1200'''   11,145  7,802   5,573   3,901   2,837   1,950   1,418   975   709
 Some usage examples
 *You want to shoot a gigapixel panorama of 175° width with a 800mm lens at f/11. You get 175*1,891 = 330,925 pixel maximum horizontal resolution.
 *You will use an APS-C format sensor in portrait orientation for this panorama. A 800mm lens has a FoV of 1.1° in that case, which at f/11 gives 2080 pixels or app. 6 megapixels. Applying the 70% rule to compensate for bayer interpolation blur indicates that 12 megapixels per image are enough.
 ==External links==
@@ Line 31: / Line 39: @@
 *wikipedia on [[w:Angular resolution|Angular resolution]]
 *[http://www.kenrockwell.com/tech/focus.htm Ken Rockwell's page] on Selecting the Sharpest Aperture

@@ Line 11: / Line 11: @@
 ==Resolution==
 The maximum obtainable resolution is limited by diffraction according to the [[w:angular resolution|Rayleigh criterion]]. Since this criterion defines the angular resolution it can be directly used for zoomable panoramas neglecting sensor sizes etc. By simply dividing the panorama [[Field of View]] (FoV) by the angular resolution we get the maximum possible pixel resolution. For an average value we take the wavelength of light ''λ'' = 550nm = 5.5*10<sup>-4</sup>mm. The resulting formula is:
-  <math> pixel resolution = /frac {FoV}{asin \left(\frac{1}{1490*D}\right)}</math>
+  <math> pixel resolution = \frac{FoV}{asin\left(\frac{1}{1490*D}\right)}\,\!</math>
 ''D'' is the diameter of the lens' aperture, which is the focal length in mm divided by the f-number. The following table shows the maximum angular resolution in pixels/degree which is obtainable by a given focal length (vertical) and f-number (horizontal):
             '''2.8      4     5.6       8      11      16      22    32    44'''